The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking...

State the null and alternate hypotheses.H0: Myers-Briggs preference and profession are not independent.H1: Myers-Briggs preference and profession are not independent.

H0: Myers-Briggs preference and profession are independent.H1: Myers-Briggs preference and profession are not independent.    

H0: Myers-Briggs preference and profession are independent.H1: Myers-Briggs preference and profession are independent.

H0: Myers-Briggs preference and profession are not independent.H1: Myers-Briggs preference and profession are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What sampling distribution will you use?

chi-square

binomial    

uniform

normal

Student's t What are the degrees of freedom?    (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)      (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.